Question

question
solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(MLK\) with \(\angle M = 31^{\circ}\), \(\angle L=90^{\circ}\), and hypotenuse \(MK = 96\). We use the cosine function. The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 31^{\circ}\), the adjacent side to \(\angle M\) is \(ML=x\), and the hypotenuse \(MK = 96\). So, \(\cos(31^{\circ})=\frac{x}{96}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(31^{\circ})=\frac{x}{96}\) by \(96\). We get \(x = 96\times\cos(31^{\circ})\).
We know that \(\cos(31^{\circ})\approx0.8572\). Then \(x=96\times0.8572\).
\(x = 82.3\) (rounded to the nearest tenth)

Answer:

\(x = 82.3\)